A generalized FKG-inequality for compositions

TL;DR

This paper establishes a generalized FKG-inequality for compositions, extending classical inequalities like Alexandrov-Fenchel and Teissier's to a broader combinatorial and geometric context.

Contribution

It introduces a new FKG-type inequality for compositions, broadening the scope of classical geometric inequalities to combinatorial lattice structures.

Findings

Proves a Fortuin-Kasteleyn-Ginibre-type inequality for compositions.

Generalizes Alexandrov-Fenchel inequality for mixed volumes.

Extends Teissier's inequality for mixed covolumes.

Abstract

We prove a Fortuin-Kasteleyn-Ginibre-type inequality for the lattice of compositions of the integer n with at most r parts. As an immediate application we get a wide generalization of the classical Alexandrov-Fenchel inequality for mixed volumes and of Teissier's inequality for mixed covolumes.